Now that I know the exact pinout of CN7, I decided to do a little test this morning: tie pin 6 to GND and see if any serial data would show up on pin 4 (TX) when powering the air conditioner, switching it on/off, or pressing a button on the remote control.
To my surprise, and sadly, not data showed up on pin 4. I repeated the test a few several times, checked my connections 3 or 4 times but still nothing. I had hoped that by putting pin 6 low to enable H-LINK connectivity function, the air conditioner would start sending data on pin 4 whenever its state or settings were changed... 

So, I decided to try to send data on pin 2 (RX) and see if anything appeared on pin 4 before wrapping things up. I connected my FTDI USB to TTL Serial Adapter, hooked up my oscilloscope and launched Termite.

I didn't adjust Termite settings and simply sent a "0". And as you can see in the photo above, something showed up on pin 2!
So I tweaked my oscilloscope settings to measure a full frame, resent a "0" via Termite, captured data and exported as a CSV. After spending some time in Excel, I discovered it's a simple serial communication (see file Measurement (2020_01_11).xlsx for details).

• 9600 bauds
• 8 bits
• odd parity
• 1 start bit
• 1 stop bit 

What I received from the air conditioner after sending a "0" was "NG P=01 C=FFFE " (the last character after E is 0x0D, Carriage Return). I then went back to Termite, changed the settings, and I got the same result.

I tried sending other random commands and whatever I got from the air conditioner, but I always received the same result. Interestingly, even when pin 6 isn't tied to GND, the behavior remains the same.

I've kind of reached a dead end here, so I guess my next move will be to get my hands on a RAC adapter and a wall remote control to do some deeper reverse engineering.